Question

two cylindrical capacitor has radii of inner and outer plates as (a,b) and (c,d).If they have same length and ame capacitance,then
1.a/b=c/d
2. a*b=c*d
3.a+b/2=c+d/2
4.a*c=b*d
plz explain the correct option in detail

Answer 1

Given :

▪ Two cylindrical capacitor has radii of inner and outer plates as (a,b) and (c,d).

▪ They have same length and same capacitance.

To Find :

▪ Relation b/w their inner and outer radii.

Formula :

→ Let consider a cylindrical capacitor of length L.

• Inner radius = X
• Outer radius be = Y

→ Formula of capacitance of cylindrical capacitor is given by

$\bigstar\:\underline{\boxed{\bf{\pink{C=\dfrac{2\pi\epsilon_o L}{ln{\large{(}}\frac{Y}{X}{\large{)}}}}}}}$

Calculation :

$\dashrightarrow\sf\:C_A=C_B\\ \\ \dashrightarrow\sf\:\dfrac{2\pi\epsilon_o L}{ln{\large{(}}\frac{b}{a}{\large{)}}}=\dfrac{2\pi\epsilon_o L}{ln{\large{(}}\frac{d}{c}{\large{)}}}\\ \\ \dashrightarrow\sf\:ln{\large{(}}\dfrac{b}{a}{\large{)}}=ln{\large{(}}\dfrac{d}{c}{\large{)}}\\ \\ \dashrightarrow\sf\:\dfrac{b}{a}=\dfrac{d}{c}\\ \\ \dashrightarrow\underline{\boxed{\bf{\green{\dfrac{a}{b}=\dfrac{c}{d}}}}}\:\gray{\bigstar}$